6 problems

Inherited correspondence conjecture. The maximum number of edges in a subgraph $H$ of $G$ in which every collection of disjoint cycles covers at most $k$ vertices equals the larges…

Let $\mathbb{K}$ be a field of characteristic $2$ with more than $2$ elements. Let $\mathcal{V}$ be a $\overline{2}$-spec subspace of $\operatorname{M}_n(\mathbb{K})$, with…

Let $\mathbb{K}$ be a field of characteristic $2$ with more than $2$ elements. Let $\mathcal{V}$ be a $\overline{1}^\star$-spec subspace of $\operatorname{M}_n(\mathbb{K})$ with ……

Let $\mathbb{K}$ be a field of characteristic $2$ with more than $2$ elements, and let $\mathcal{V}$ be a $1^\star$-spec subspace of $\operatorname{M}_n(\mathbb{K})$. Characteristi…

Let $\mathbb{K}$ be a field of characteristic $2$ with more than $2$ elements, and let $\mathcal{V}$ be a $2$-spec subspace of $\operatorname{M}_n(\mathbb{K})$. Characteristic-two…

Let $V$ be a $1$-spec subspace of $\operatorname{M}_n(\mathbb{K})$ such that … Assume $n>4$. A linear subspace $W$ of $\operatorname{M}_n(\mathbb{K})$ has a trivial spectrum if no…